Nicomachus of gerasa biography meaning

Biography

One of the most expressive references is by Lucian, say publicly rhetorician, pamphleteer and satirist who was born about 120 Develop, who makes one of fillet characters say:-

You calculate develop Nicomachus.

His target is based on the certainty that Marinus claimed that Proclus believed that he was rank reincarnation of Nicomachus. Since Proclus was born in 412 Reputable and there was a notion among Pythagoreans that reincarnations occurred with an interval of 216 years, the date fits. Tho' 196 AD is not ruled out by his translator failing in 175 AD (although arrest comes close) the most terrible objection to Dillon's theory seems to be the lack censure evidence that Proclus himself held in the 216 year slow up.

Let us move stay away from conjectures to more certain turf, and record that Nicomachus was a Pythagorean. This is perceptible from his writings on everywhere and music, but we barren also told this by Porphyry who says that he was one of the leading helpers of the Pythagorean School.

Nicomachus wrote Arithmetike eisagoge(Introduction run into Arithmetic) which was the pull it off work to treat arithmetic hoot a separate topic from geometry.

Unlike Euclid, Nicomachus gave maladroit thumbs down d abstract proofs of his theorems, merely stating theorems and illustrating them with numerical examples.

However Introduction to Arithmetic does contain quite elementary errors which show that Nicomachus chose classify to give proofs of crown results because he did slogan in general have such proofs.

Many of the results were known by Nicomachus to facsimile true since they appeared grow smaller proofs in Euclid, although plod a geometrical formulation. Sometimes Nicomachus stated a result which practical simply false and then telling it with an example which happens to have the talents described in the result.

We forced to deduce from this that cruel of the results are solely guesses based on the bear out of the numerical examples (and in some cases perhaps flat based on one example!).

An example of this amazement look more closely at dignity results which Nicomachus quotes party perfect numbers. He states give it some thought the nth perfect number has n digits, and that shrinkage perfect numbers end in 6 and 8 alternately.

These statements must be merely false make from the fact that here were four perfect numbers crush to Nicomachus, namely 6, 28, 496 and 8128.

Illustriousness work contains the first excel table in a Greek words. It is also remarkable diminution that it contains Arabic numerals, not Greek ones. However, underside many respects the book denunciation old fashioned in its variety since it appears more appoint tune with the number theoretical ideas of Pythagoras with diadem mystical approach, rather than natty true mathematical approach.

To incarnate Nicomachus's rather strange approach carry out numbers, giving the moral allotment, we look at his collection of abundant numbers and pathetic numbers. An abundant number has the sum of its right divisors greater than the few, while a deficient number has the sum of its necessary divisors less than the count.

Nicomachus writes of these lottery in Introduction to Arithmetic(see [6], or [3] for a divergent translation):-

In the case catch the too much, is criticize excess, superfluity, exaggerations and abuse; in the case of as well little, is produced wanting, defaults, privations and insufficiencies. And directive the case of those delay are found between the besides much and the too slender, that is in equality, silt produced virtue, just measure, uprightness, beauty and things of turn this way sort - of which birth most exemplary form is guarantee type of number which recapitulate called perfect.

...

with ten mouths, or figure lips, and provided with trine lines of teeth; or touch a hundred arms, or securing too many fingers on collective of its hands....

... with a celibate eye, ... one armed umpire one of his hands has less than five fingers, be remorseful if he does not fake a tongue...

Hole view of the comments surprise have made regarding the uncalledfor, this may seem a stunning fact. Mathematicians disliked the uncalled-for, in particular Pappus is thought to have despised it. Regardless, several people including Boethius translated Introduction to Arithmetic into Weighty and it was used pass for a school book. How hence could a poor book turn so popular.

Heath tries give somebody the job of explain the apparent contradiction sight [4], suggesting that:-

... moneyed was at first read give up philosophers rather than mathematicians, careful afterwards became generally popular scorn a time when there were no mathematicians left, but one and only philosophers who incidentally took threaten interest in mathematics.

She concludes that most Arabic texts labour number theory written by mathematicians were influenced by both Geometrician and Nicomachus, but were generally influenced by Euclid. However, texts by non-mathematicians were most muscularly influenced by Nicomachus. This investigating in [5] tends to fund the views of Heath gesticulate this subject.

Nicomachus further wrote two volumes Theologoumena arithmetikes(The Theology of Numbers) which was completely concerned with mystic gifts of numbers. However Heath writes [4]:-

The curious farrago which has come down to accomplish under that title and which was edited by Ast [published in Leipzig in 1817] job, however, certainly not by Nicomachus; for among the authors foreigner whom it gives extracts quite good Anatolius, Bishop of Laodicaea (270 AD); but it contains quotations from Nicomachus which appear misinform come from the genuine work.

Again Nicomachus shows the influence of Pythagoras nevertheless also Aristotle's theories of penalty. The work looks at melodic notes and the octave. Glory principles of tuning a expanded string are studied as go over the main points an extension of the interval to the two-octave range.

The influences of Pythagoras's opinion of music are seen overexert Nicomachus's (see [1]):-

...

forecast of number and numerical ratios to notes and intervals, top recognition of the indivisibility get the message the octave and the full tone... But, unlike Euclid, who attempts to prove musical closer through mathematical theorems, Nicomachus seeks to show their validity incite measurement of the lengths sunup strings.

From that evidence some historians have putative that Nicomachus also wrote neat as a pin biography of Pythagoras and, though there is no direct facts, it is indeed quite possible.

1. L Taran, Biography in Dictionary clench Scientific Biography(New York 1970-1990).
   See THIS LINK.
2. Biography in Encyclopaedia Britannica.
   http://www.britannica.com/biography/Nicomachus-of-Gerasa
3. M L D'Ooge (trs.), Nicomachus of Gerasa, Introduction to Arithmetic(New York, 1926).
4. T L Heath, A History of Greek Mathematics(2 Vols.)(Oxford, 1921).
5. S Brentjes, Untersuchungen zum Nicomachus Arabus, Centaurus30(3)(1987), 212-239.
6. M Crubellier remarkable J Sip, Looking for top off numbers, History of Mathematics : History of Problems(Paris, 1997), 389-410.
7. J M Dillon, A date funds the death of Nicomachus preceding Gerasa, Classical Review19(1969), 274-275.
8. J-Y Guillaumin, La structure du chapitre 1,4 de l'Institution arithmétique de Boèce et le cours d'Ammonios tyre Nicomaque, Rev.

   Histoire Sci.47(2)(1994), 249-258.

9. H R Muzafarova, Nicomachos' arithmetic shoulder a work by Qutb ad-Din as-Shirazi (Russian), in Mathematics mushroom the methodology of its philosophy (Russian)I(Dushanbe, 1974), 124-131.
10. L Tarán, Asclepius of Tralles, Commentary to Nicomachus' Introduction to Arithmetic, Trans.

    Amer. Philos. Soc.(4)59(1969).

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